","mla":"Prokhorov, Yu. V., Götze, Friedrich, and Ulyanov, V. V. “ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES”. THEORY OF PROBABILITY AND ITS APPLICATIONS 62.1 (2018): 98-116."},"type":"journal_article","external_id":{"isi":[]},"dc":{"rights":["info:eu-repo/semantics/closedAccess"],"type":["info:eu-repo/semantics/article","doc-type:article","text"],"publisher":["Siam Publications"],"title":["ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1137/S0040585X97T988514","info:eu-repo/semantics/altIdentifier/issn/0040-585X","info:eu-repo/semantics/altIdentifier/issn/1095-7219","info:eu-repo/semantics/altIdentifier/wos/000432323500008"],"description":["We obtain upper bounds for the absolute values of the characteristic functions of the kth powers of asymptotically normal random variables. Estimates are proved for the case when asymptotically normal random variables are normalized sums of independent identically distributed summands with a \"regular\" distribution. Possible generalizations are considered. The estimates extend the results of previous studies, where for the distributions of the summands, the presence of either a discrete or an absolutely continuous component was required. The proofs of the bounds are based on the stochastic generalization of the I. M. Vinogradov mean value theorem, which is also obtained in the present paper."],"source":["Prokhorov YV, Götze F, Ulyanov VV. ON BOUNDS FOR CHARACTERISTIC FUNCTIONS OF POWERS OF ASYMPTOTICALLY NORMAL VARIABLES. THEORY OF PROBABILITY AND ITS APPLICATIONS. 2018;62(1):98-116."],"subject":["powers of random variables","bounds for characteristic functions","the","Vinogradov mean value theorem","stochastic generalization"],"identifier":["https://pub.uni-bielefeld.de/record/2920354"],"date":["2018"],"creator":["Prokhorov, Yu. V.","Götze, Friedrich","Ulyanov, V. V."],"language":["eng"]}}]